Finger tapping movements of Parkinson's disease patients automatically rated using nonlinear delay differential equations.

Parkinson's disease is a degenerative condition whose severity is assessed by clinical observations of motor behaviors. These are performed by a neurological specialist through subjective ratings of a variety of movements including 10-s bouts of repetitive finger-tapping movements. We present here an algorithmic rating of these movements which may be beneficial for uniformly assessing the progression of the disease. Finger-tapping movements were digitally recorded from Parkinson's patients and controls, obtaining one time series for every 10 s bout. A nonlinear delay differential equation, whose structure was selected using a genetic algorithm, was fitted to each time series and its coefficients were used as a six-dimensional numerical descriptor. The algorithm was applied to time-series from two different groups of Parkinson's patients and controls. The algorithmic scores compared favorably with the unified Parkinson's disease rating scale scores, at least when the latter adequately matched with ratings from the Hoehn and Yahr scale. Moreover, when the two sets of mean scores for all patients are compared, there is a strong (r = 0.785) and significant (p<0.0015) correlation between them.

Ansatz library for global modeling with a structure selection.

The information contained in a scalar time series and its time derivatives is used to obtain a global model for the underlying dynamics. This model provides a description of the time evolution of the system studied in a space spanned by the time series and its successive time derivatives which is expected to be equivalent to the original phase space. Differential models are, in general, very complicated and do not necessarily capture all properties of the original dynamics. The possibility of choosing a form among an ansatz library for the original system which allows a structure selection for the differential model is considered. It allows for the reduction of the complexity of the model and the recovery of the right property when the differential model is transformed back into the space associated with the ansatz.